A popcorn container at a movie theatre has the shape of a frustum of a pyramid. With dimensions as indicated, find the volume (capacity) of the container.
The volume (capacity) of the container.
The popcorn container at a movie theatre is in the shape of a frustum of a pyramid as shown below
A pyramid is made by connecting a base to an apex. The base is flat with straight edges, no curves, hence, a polygon and all other faces are triangles.
A regular pyramid is a pyramid whose base is a regular polygon and whose lateral edges are all congruent.
A frustum of a pyramid is the portion of a pyramid that lies between its base and a parallel plane that intersects the pyramid.
The volume of a pyramid having a base area and an altitude of length is given by .
According to the Pythagorean theorem, in a right-angled triangle
In a regular pyramid, the lengths of the apothem of the base, the altitude , and the slant height satisfy the Pythagorean Theorem; that is, .
i) Calculate the volume of the bigger pyramid .
ii) Calculate the volume of the smaller pyramid .
iii) Subtract the two to get the volume of the frustum .
Calculating the volume of the bigger pyramid
with base as a square of side and height as .
The area of the square base is
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